ASTR 1200 Announcements Second problem set due Lecture

ASTR 1200 Announcements Second problem set due Lecture Notes going up on the website First Exam October 7 Website http: //casa. colorado. edu/~wcash/APS 1200. html

Summary: Sun as a Star • Formed from cloud 4. 6 x 109 years ago • Collapsed to present size – stabilized by nuclear reactions • • Emits 4 x 1026 W Runs on proton-proton chain and CNO cycle Now 20% brighter Turbulent upper envelope Magnetic Fields from Differential Rotation Sunspots, Corona, Solar Wind Activity Cycle 11 years

Stars are grouped in Galaxies • Sun and all the stars we see are part of Milky Way Galaxy • We all orbit a common center • Sun is 3 x 1020 m from center of MW You are here Each star orbits center Disk Stability Again

The Light Year Light Travels at 300, 000 km/s (186, 000 miles/s = 3 x 108 m/s) That’s one foot per nanosecond One Year is 3. 15 x 107 seconds long In one year light travels 3. 15 x 107 x 3 x 108 = 1016 m This is the definition of a light year. Prox Cen is at 4 ly.

The Parsec Astronomers use the parsec as a measure of distance 1 pc = 3 ly 1 pc = 3 x 1016 m Origin of parsec comes from method of measuring distance

Each Star Orbits the Center

How Long does that Take? Takes about a hundred million years to circumnavigate the galaxy

Star Names • Arabic Names – Antares, Capella, Mira, etc. • Constellations a Orionis, b Cygni, … then 49 Ori, 50 Ori, etc. • Catalogues HD 80591, SAO 733421, etc • RA and Dec – just position in the sky

Proper Motion 2003 All stars move Nearby stars move faster Appear to move against fixed field 1900 Can Take Many Years Use Old Photographic Plates

Parallax I year cycle

The Parsec 1 parsec 1 AU 1 arcsecond 360 degrees in circle 60 arcminutes per degree 60 arcseconds per arcminute 200, 000 AU = 1 parsec = 3 x 1016 m parsec ---- parallax second

Brightness Around the sky stars vary in brightness and in color. Brightness is the result of two factors 1. Intrinsic Luminosity 2. Distance d Star Emits N photons per second Each Sphere has area A=4 pd 2 Brightness is photons/m 2/s

Brightness (2) Brightness e. g. 10 -12 Watts/m 2 Simple and easy to understand If your eye is 10 -4 m 2, then it collects 10 -16 W 4 stars at 10 -12 W/m 2 together have 4 x 10 -12 W/m 2 But this would be too easy for astronomers. We use a brightness system invented by Ptolemy in the 400’s

The Magnitude System Ptolemy Broke Stars into 5 magnitude groups m=1 the brightest, m=5 the faintest In 1700’s it was found this was a logarithmic scale, as that is how the naked eye responds. Also, faintest were about 100 x fainter than brightest. Break the factor of 100 into 5 equal factors: Start with Vega Polaris 2. 51 x fainter 2. 5 x fainter than Polaris 2. 5 x fainter than that etc m=1 m=2 m=3 m=4

Magnitudes (2) Every 5 magnitudes is a factor of 100 m=5 is 100 times fainter than m=0 m=10 is 100 x 100 =10, 000 times fainter than m=0 m=15 is (100)3 = 1 million times fainter than m=0 Sun m=-26. 5 Full Moon m=-13 Venus m=-4 Sirius m=-1. 5 Vega m=1 Polaris m=2 Faintest Visible m=6 Faintest Detected m=28 Works only in the visible. Really inconvenient in modern astronomy because we observe across the spectrum from radio to gamma rays.

Absolute Magnitude The magnitude a star would have were it at 10 pc We see a star of magnitude m=10 at 100 pc. What would be its magnitude (M) if it were at 10 pc instead of 100 pc? At 10 times closer the star would be 100 x brighter = 5 magnitudes M = 10 -5 = 5

Clicker A 5 magnitude difference means a factor of 100 in flux. By what factor do the fluxes differ between two stars of 20 magnitudes difference? a) 2. 51 b) 20 c) 400 d) 10, 000 e) 100, 000

Answer 5 magnitudes difference is a factor of 100. By what factor do the fluxes differ between two stars of 20 magnitudes difference a) 2. 51 b) 20 c) 400 d) 10, 000 20 magnitudes is four factors of 10 , which is 10 e) 100, 000 2 8

Nature of Light is a flux of particles called photons Each photon is both a particle and a wave (a packet of waves) 250 years after Newton we still don’t understand it Electromagnetic Theory (Maxwell’s Equations) 1860’s Quantum Electrodynamics 1948 Feynman Each photon has: direction wavelength polarization

Light Waves l lambda is lower case Greek “L” stands for length Each photon is a sine wave moving at the speed of light Wavelength is usually measure in Angstroms 1Å = 10 -8 cm =10 -10 m about the diameter of an atom. And 10Å = 1 nm Electric and Magnetic Fields Sloshing Back And Forth

Color Wavelength Determines Color of Light Color is the eye’s response to different wavelengths Color is a physiological effect A photon can have any wavelength RED YELLOW VIOLET 7000Å 5500Å 4000Å

Electromagnetic Spectrum visible is tiny chunk of em spectrum

Parts of EM Spectrum Radio Infrared Visible Ultraviolet X-ray Gamma-ray l > 1 mm (107 A) 1 mm> l > 10000 A 10, 000 A > l > 3500 A > l > 100 A > l > 0. 1 A > l

Clicker • What range of wavelength can the average human eye see and what color is each side of the spectrum? A) 400 nm-800 nm, redder to bluer B) 500 nm-700 nm, bluer to redder C) 400 nm-700 nm, bluer to redder D) 300 nm-600 nm, redder to bluer E) None of the above

Answer • What range of wavelength can the average human eye see and what color is each side of the spectrum? A) 400 nm-800 nm, redder to bluer B) 500 nm-700 nm, bluer to redder C) 400 nm-700 nm, bluer to redder D) 300 nm-600 nm, redder to bluer E) None of the above Answer: C

Speed of Light c = 3 x 108 m/s That’s a very odd statement 2 cars at 65 mph 1 car at 130 mph Cover same distance in same amount of time The Relative speeds are the same

Relativity. 8 c Clearly Approaching each other at 1. 6 c NO!!! per Einstein v always less than c if velocities << c, then v=v 1+v 2 (Concept of time and space changes)

Frequency l l Moves l during each cycle Frequency is the number of cycles per second, n Moves distance l for each of n cycles each second Greek “nu”

Frequency (2) 300 MHz = 1 m wavelength Yellow Light = 600 trillion Herz

Question • An x-ray has a wavelength of 100Å • (10 nm, 1 x 10 -8 m). What is it's frequency, in cycles per second? (aka Hertz) • A. 3 x 1016 • B. 1. 5 x 1016 • C. 3 x 1013 • D. 1. 5 x 1013

Question • An x-ray has a wavelength of 100Å (10 nm, 1 x 10 -8 m). What is it's frequency, in cycles per second? (aka Hertz) • A. 3 x 1016 • B. 1. 5 x 1016 • C. 3 x 1013 • D. 1. 5 x 1013 • Answer: A. (3 E 8 m/s)/(1 E-8 m)=3 E 16 Hz

Energy of a Photon h = 6. 63 x 10 -34 J s Planck’s Constant energy of yellow photon Sunlight is 104 W/m 2 Outside we have 1023 photons/m 2/s hit us

Question • How many times more energy is there in an x-ray photon at 100 A than the infrared light photons emitted by every living human? (Assuming 10, 000 nm wavelength of infrared light). • A. Ten times as powerful. • B. A hundred times more powerful. • C. A thousand times more powerful. • D. 1 x 1012 (a trillion) times more powerful. • E. 1 x 1015 (a quadrillion) times more powerful.

Question • How many times more energy is there in an x-ray photon at 100 A than the infrared light photons emitted by every living human? (Assuming 10, 000 nm wavelength of infrared light). • A. Ten times as powerful. • B. A hundred times more powerful. • C. A thousand times more powerful. • D. 1 x 1012 (a trillion) times more powerful. • E. 1 x 1015 (a quadrillion) times more powerful. • Answer: C. 10, 000 nm/10 nm = 1000

Spectroscopy Spectrum is plot of number of photons as a function of wavelength Tells us huge amounts about nature of object emitting light.

Thermal Radiation Planck’s Law Temperature Determines Where Spectrum Peaks Position of Peak Determines Color

Blue is Hotter than Red Optically Thick, But hot Sun almost “white hot” Burner “red hot” Desk “black hot” Ice Cube “black hot”

Question A star with a temperature of 100, 000 K has what color to the naked eye? a) White b) Yellow c) Orange d) Red

Wien’s Law Å (T in Kelvin) As T rises, l drops Bluer with temperature 300 K 5500 106 100, 000 A 5500 30 Earth Sun X-ray source

Question • How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500 K) • A. Twice as long • B. Half as long • C. Four times as long • D. A fourth as long

Question • How many times smaller would the peak wavelength be for a star twice as hot as the Sun? (Remember the sun is 5500 K) • A. Twice as long • B. Half as long • C. Four times as long • D. A fourth as long • Answer: B. Since peak wavelength is a function of the inverse of temperature, doubling the temp of a star would cause it's peak wavelength to cut in half.

Stefan-Boltzman Law s = 5. 67 x 10 -8 W/m 2/K 4 A is area in m 2 T in Kelvins Example: The Sun L = 5. 7 x 10 -8 x 4 x 3. 14 x (7 x 108 m)2 x (5500 K)4 = 4 x 1026 W 4 x 1026 Watts = 100 billion Mega. Watts!!

Question If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? a) 2 b) 4 c) 8 d) 16 e) 32

Question If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? a) 2 b) 4 c) 8 d) 16 = 24 e) 32

Emission Lines Electron Drops Energy Levels of H Photon Escapes Can Only Happen Between Certain Pre-determined orbitals Each Element Has Different Orbitals So Each Element Has Different Lines Spectrum of Hydrogen

Absorption Lines Light moving through cold gas can have photons removed Creates dark wavelengths called absorption lines

Question A star is viewed through a far away hydrogen gas cloud, what kind of spectrum can we expect to see? A) Absorption only B) Emission only C) Continuum only D) Emission and Continuum E) Absorption and Continuum

Stars Come in Different Colors

Stellar Temperature Stars come in different sizes and temperatures. Can the two be linked?

Question You see three stars up in the sky. One is bigger than the others and red, one is yellow, and one is white. Which one peaks at a higher frequency? • A)Red • B)Yellow • C)White • D)I need to know how far away they are

Stellar Classification Full range of surface temperatures from 2000 to 40, 000 K Spectral Classification is Based on Surface Temperature Hottest O B A F G K { } Oh Be A Fine Gal Kiss Me Guy Each Letter has ten subdivisions from 0 to 9 0 is hottest, 9 is coolest M Coolest

The Spectral Types O Stars of Orion's Belt >30, 000 K Lines of ionized helium, weak hydrogen lines <97 nm (ultraviolet)* B Rigel 30, 000 K -10, 000 K Lines of neutral helium, moderate hydrogen lines 97 -290 nm (ultraviolet)* A Sirius 10, 000 K -7, 500 K Very strong hydrogen lines 290 -390 nm (violet)* F Polaris 7, 500 K 6, 000 K Moderate hydrogen lines, moderate lines of ionized calcium 390 -480 nm (blue)* G Sun, Alpha Centauri A 6, 000 K 5, 000 K Weak hydrogen lines, strong lines of ionized calcium 480 -580 nm (yellow) K Arcturus 5, 000 K 3, 500 K Lines of neutral and singly ionized metals, some molecules 580 -830 nm (red) M Betelgeuse, Proxima Centauri <3, 500 K Molecular lines strong >830 nm (infrared) *All stars above 6, 000 K look more or less white to the human eye because they emit plenty of radiation at all visible wavelengths.

Stellar Classification (2) Sun a Cen Sirius Antares Rigel G 2 + K 5 A 1 M 1 B 8 O 5 B 5 A 5 F 5 G 5 K 5 M 5 40, 000 K 15, 500 8500 6580 5520 4130 2800 Letters are odd due to confusion in sorting out temperature scale between 1900 and 1920